| Description |
1 online resource (xii, 447 pages) : illustrations (some color) |
| Physical Medium |
polychrome |
| Description |
text file |
| Bibliography |
Includes bibliographical references (pages 437-444) and index. |
| Contents |
Ch. 1. Introduction. 1.1. A brief history of dynamics. 1.2. Nonlinear Hamiltonian systems. 1.3. Dissipative nonlinear systems. 1.4. Book layout -- ch. 2. Differential geometry of flows. 2.1. Normal distance and G-functions. 2.2. Non-contact flows. 2.3. Contact flows. 2.4. Concluding remarks -- ch. 3. Global transversality in continuous dynamical systems. 3.1. Nonlinear dynamical systems. 3.2. Local and global flows. 3.3. Global transversality. 3.4. Global tangency. 3.5. Perturbed Hamiltonian systems. 3.6. Two-dimensional Hamiltonian systems. 3.7. A damped Duffing oscillator. 3.8. Global transversality to a generalized separatrix -- ch. 4. Chaotic layer dynamics. 4.1. Chaotic domains in phase space. 4.2. First integral quantity increments. 4.3. Resonance mechanism of chaotic layers. 4.4. Energy increments in perturbed Hamiltonian systems -- ch. 5. Two-dimensional stochastic layers. 5.1. Geometric description in phase space. 5.2. Approximate predictions. 5.3. Stochastic layer in a Duffing oscillator. 5.4. Conclusions and discussions -- ch. 6. Stochasticity in resonant separatrix layers. 6.1. Two-dimensional resonant separatrix layers. 6.2. 2n-dimensional resonant separatrix layers. 6.3. Resonant layers in a Duffing oscillator. 6.4. Resonant layers in a parametric pendulum -- ch. 7. Nonlinear dynamics on an equi-energy surface. 7.1. Hamiltonian systems. 7.2. Nonlinear resonance. 7.3. Energy spectrum. 7.4. Chaotic motions on an equi-energy surface. 7.5. Conclusions -- ch. 8. Stability and grazing in dissipative systems. 8.1. Equilibrium stability. 8.2. Periodic flow stability. 8.3. Local grazing bifurcation. 8.4. Global grazing bifurcation -- ch. 9. Global dynamics in two-dimensional dynamical systems. 9.1. Tangency and transversality. 9.2. Energy increment and Melnikov function. 9.3. Mapping structures. 9.4. Bifurcation scenario. 9.5. Numerical illustrations -- ch. 10. Flow switchability in discontinuous dynamical systems. 10.1. Discontinuous dynamical systems. 10.2. Passable flows. 10.3. Non-passable flows. 10.4. Tangential flows. 10.5. Flow switching bifurcations. 10.6. First integral quantity increment. |
| Summary |
This unique book presents a different point of view on the fundamental theory of global transversality, resonance and chaotic dynamics in n-dimensional nonlinear dynamic systems. The methodology and techniques presented in this book are applicable to nonlinear dynamical systems in general. This book provides useful tools for analytical and numerical predictions of chaos in nonlinear Hamiltonian and dissipative systems. All theoretical results are strictly proved. However, the ideas presented in this book are less formal and rigorous in an informal and lively manner. The author hopes the initial ideas may give some inspirations in the field of nonlinear dynamics. With physical concepts, the author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in nonlinear dynamics. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Dynamics.
|
|
Dynamics. |
|
Nonlinear systems.
|
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Nonlinear systems. |
|
Chaotic behavior in systems.
|
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Chaotic behavior in systems. |
| Genre/Form |
Electronic books.
|
| Other Form: |
Print version: Luo, Albert C.J. Global transversality, resonance and chaotic dynamics. Singapore ; Hackensack, NJ : World Scientific, ©2008 9812771115 9789812771117 (DLC) 2008299311 (OCoLC)173808086 |
| ISBN |
9789812771124 (electronic book) |
|
9812771123 (electronic book) |
|
1281911682 |
|
9781281911681 |
|
9812771115 |
|
9789812771117 |
|
